With a simple but controversial assumption and lots of supercomputer time, two geophysicists have solved a long-standing problem in geology -- why the jigsaw puzzle of crustal plates on the Earth's surface looks the way it does.

The problem, which has bedeviled the theory of plate tectonics since it was proposed nearly a half century ago, is that basic theories of fluid heating and convection say the surface should be broken into many small puzzle pieces, none larger than about 3,000 kilometers across.

Instead we see a smaller number of huge plates. One of these, the Pacific plate, spans nearly 13,000 kilometers at its widest, more than four times larger than predicted.

The scientists found that by making a simple but fundamental assumption -- that the viscosity or stiffness of the hot rock in the Earth's interior increases by a factor of 30 from top to bottom -- they could predict exactly what is observed on the surface.

This includes not only the size of the plates but also the geometry of plate boundaries and even the stability of so-called hot spots that underlie island arcs such as the Hawaiian Islands.

In their new model, upwelling of hot rock from the deep mantle and downwelling of cool rock from near the surface -- analogous to the upward movement of hot air and the downward flow of cool air in the atmosphere -- create a cyclic flow or convection cell with dimensions close to the dimensions of the tectonic plates.

Because convection in the mantle is assumed to nudge the continents around on the surface of the Earth and break them up into plates of roughly the same size as the convection cell, this model provides an explanation for why the plates are the size they are.

"This is a fundamental discovery of fluid dynamics which brings us very close to solving a major problem of geodynamics," says Mark Richards, professor of geophysics.

The feat was achieved by monopolizing a massively parallel computer at Los Alamos National Laboratory in New Mexico for nearly three weeks to perform calculations on a three-dimensional model of the Earth's mantle.

The mantle, composed of rock at high temperature and pressure, underlies the surface crust or lithosphere and extends 2,700 kilometers down to the Earth's core.

Richards and graduate student Hans-Peter Bunge, currently working at Los Alamos, will describe their model in a cover article scheduled for the Oct. 1 issue of Geophysical Research Letters.

"The amazing thing is that such a simple effect, a viscosity contrast between the upper and lower mantle, has such profound influence on what we find at the surface," Richards says.

"The size of the continents is governed by this effect and not by the structure and stickiness of the plates."

Their model also explains the stability of the Earth's hotspots -- upwellings of hot molten rock in spots that remain constant for billions of years.

The Hawaiian and Reunion Islands, as well as Yellowstone and Iceland, are examples of hot spots that have remained in the same place for a large portion of the Earth's history.

The reason, Richards says, is that these upwellings are rooted solidly in the very viscous deep mantle, near where it borders the core, and can't move.

"Our model explains why the rotation axis is static with respect to the deep mantle and to the hot spots," he says.

Bunge and Richards will continue to improve their model so that it more accurately reflects the physical details of the Earth's interior. Also, while the most recent calculations were for a mantle modeled on a scale of about 50 kilometers, they hope soon to increase the resolution to 25 kilometers.

Bunge is also developing a way to calculate the model using a cluster of inexpensive workstations, rather than 64 parallel computers of the very expensive Cray T3D toroidal supercomputer, which are available at only a few places in the world.

The work was supported by a grant from the National Science Foundation and by the Institute of Geophysics and Planetary Physics at Los Alamos.

Computer time was provided by the Advanced Computing Laboratory at LANL.